This interop call should be used when a menu item is selected by the user with click or Enter:

Win32Api.PlaySound("MenuCommand", default, PlaySoundFlags.SND_ALIAS | PlaySoundFlags.SND_ASYNC);

This interop call should be used whenever a menu or submenu appears:

Win32Api.PlaySound("MenuPopup", default, PlaySoundFlags.SND_ALIAS | PlaySoundFlags.SND_ASYNC);

Neither of the calls will hang the calling thread. Interop definitions as follows:

[Flags]
public enum PlaySoundFlags : uint
{
    SND_SYNC = 0x0000, /* play synchronously (default) */
    SND_ASYNC = 0x0001, /* play asynchronously */
    SND_NODEFAULT = 0x0002, /* silence (!default) if sound not found */
    SND_MEMORY = 0x0004, /* pszSound points to a memory file */
    SND_LOOP = 0x0008, /* loop the sound until next sndPlaySound */
    SND_NOSTOP = 0x0010, /* don't stop any currently playing sound */
    SND_NOWAIT = 0x00002000, /* don't wait if the driver is busy */
    SND_ALIAS = 0x00010000, /* name is a registry alias */
    SND_ALIAS_ID = 0x00110000, /* alias is a predefined ID */
    SND_FILENAME = 0x00020000, /* name is file name */
    SND_RESOURCE = 0x00040004, /* name is resource name or atom */
    SND_PURGE = 0x0040, /* purge non-static events for task */
    SND_APPLICATION = 0x0080, /* look for application specific association */
    SND_SENTRY = 0x00080000, /* Generate a SoundSentry event with this sound */
    SND_RING = 0x00100000, /* Treat this as a "ring" from a communications app - don't duck me */
    SND_SYSTEM = 0x00200000, /* Treat this as a system sound */
}

public static class Win32Api
{
    [DllImport("winmm.dll", EntryPoint = "PlaySoundW", ExactSpelling = true, CharSet = CharSet.Unicode, CallingConvention = CallingConvention.Winapi, SetLastError = false)]
    [return: MarshalAs(UnmanagedType.Bool)]
    public static extern bool PlaySound(
        [In, MarshalAs(UnmanagedType.LPWStr)] string pszSound,
        [In] IntPtr hmod,
        [In] PlaySoundFlags fdwSound);
}